Curve-based deployment for barrier coverage in wireless sensor networks

This paper studies deterministic sensor deployment for barrier coverage in wireless sensor networks. Most of existing works focused on line-based deployment, ignoring a wide spectrum of potential curve-based solutions. We, for the first time, extensively study the sensor deployment under a general setting. We first present a condition under which the line-based deployment is suboptimal, revealing the advantage of curve-based deployment. By constructing a contracting mapping, we identify the characteristics for a deployment curve to be optimal. Based on the optimal deployment curve, we design sensor deployment algorithms by introducing a new notion of distance-continuous. Our findings show that i) when the deployment curve is distance-continuous, the proposed algorithm is optimal in terms of the vulnerability corresponding to the deployment, and ii) when the deployment curve is not distance-continuous, the approximation ratio of the vulnerability corresponding to the deployment by the proposed algorithm to the optimal one is upper bounded by \min(π, \frac{||\widetilde{AB}||}{||\widetilde{AGB}||}\frac{2n+\sqrt{2}-1}{2n} ), where ||\widetilde{AB}|| and ||\widetilde{AGB}|| are some constants, and n is the number of sensors. We generalize the study to the heterogeneous sensing model, and show that the proposed algorithm can provide close-to-optimal performance. Extensive numerical results corroborate our analysis.